Singapura

Did you turn the tv on? Sorry, I couldn't resist. It does sound like a bad chip. You may want to clean all the contacts in the cartridge bay. Also, check if you get a black screen on another tv and with another RF modulator.

Maybe you put the cartridge in backward

I won my Atari 2600 in a Pac man arcade contest. Off course the cartridge was Pac Man. Played it till both joysticks broke. Bought new sticks then played some more. In the end I could play unlimited time. Loved it! Space invaders came a close second.

3D Monster Maze for the ZX81.